System and method for calibrated spectral domain optical coherence tomography and low coherence interferometry

ABSTRACT

Systems and methods for enhancing spectral domain optical coherence tomography (OCT] are provided. In particular, a system and method for calibration of spectral interference signals using an acquired calibration signal are provided. The calibration signal may be logarithmically amplified to further improve the accuracy of the calibration. From the calibration signal, a series of more accurate calibration data are calculated. An acquired spectral interference signal is calibrated using these calibration data. Moreover, systems that include logarithmic amplification of the spectral interference signal and variable band-pass filtering of the spectral interference signal are provided. Such systems increase the dynamic range and visualization capabilities relative to conventional spectral domain OCT systems.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 61/265,571, filed on Dec. 1, 2009, and entitled“SYSTEM AND METHOD FOR ENHANCED SPECTRAL DOMAIN OPTICAL COHERENCETOMOGRAPHY AND LOW COHERENCE INTERFEROMETRY”.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with United States Government support awarded bythe following agency: National Institutes of Health NIH AR44812, NIHHL55686, NIH EB02638/HL63953, NIH AR46996, and NIH EB00419. The UnitedStates Government has certain rights in this invention.

FIELD OF THE INVENTION

The field of the invention is systems and methods for optical coherencetomography (“OCT”) and low coherence interferometry (“LCI”). Moreparticularly, the invention relates to systems and methods for enhancedspectral domain OCT and LCI.

BACKGROUND OF THE INVENTION

Optical coherence tomography (“OCT”), which is based on low coherenceinterferometry, measures the depth-resolved back-reflections orback-scattering from an object, for example a biological tissue. OCT canprovide up to sub-micron-level image resolution, and at or abovevideo-rate image capturing speed. OCT has demonstrated substantialpotential as a minimally-invasive medical imaging modality. Early-stageOCT techniques alter the optical path length in the reference arm of aninterferometer to introduce an optical group delay and records theinterferogram time sequentially, which is commonly referred to as thetime domain OCT (“TD-OCT”).

Recently, a group of alternative OCT approaches has attractedconsiderable attention since they have demonstrated extremely highimaging speed without any mechanical movement in the reference arm thatdrastically alleviates the complexity of scan mechanics used in TD-OCT.This group of approaches can be generally categorized as spectral domainOCT (“SD-OCT”) as these techniques all record the spectralinterferograms that can be converted to depth-resolved backreflectionsby Fourier transform. Although spectral interferometry dates back to theoriginal work of Michelson, Fourier transform approaches in terms ofSD-OCT have only recently been applied to OCT. SD-OCT is generallydivided into two general techniques: swept source OCT (“SS-OCT”); andFourier domain OCT (“FD-OCT”), or spectral radar. The light sources alsodiffer with different OCT operational modes. TD-OCT and FD-OCT use awideband source, whereas SS-OCT usually utilizes a swept or tunablelaser source.

For the calibration of SD-OCT signals, a variety of methods have beenexplored. Some of the most recognizable methods include using a fixedfilter to pick up a specific wavelength as a point reference. Thismethod can dynamically compensate the instability of the starting pointof the sweeping but requires high repeatability of the spectrum. Anothermethod includes using a Fabry-Perot (“FP”) interferometer or etalon togenerate a frequency, f, comb function or a wavenumber, k, combfunction. That is, while the laser wavelength is sweeping, the generatedfrequency or wavenumber comb function is a series of pulses with a fixedinterval between adjacent two pulses. Similar to the FP method, aMach-Zehnder interferometer (“MZI”) can be used to generate a frequencycomb function, which may also be referred to as a frequency clock.Unlike the FP clock, the MZI clock is a sinusoid type fringe. This meansthat the crossing points, which are those points where the fringe signalcrosses zero or any non-zero DC level, can also be determined, whichprovides twice the reference points than a FP clock with the same freespectral range (“FSR”). Balanced detection techniques are not easilyimplemented in the FP method, which leads to more phase errors in thecalibration signal, as well as the potential for excess noise.

Many sophisticated swept laser sources provide a non-linearwavenumber-time (“k-t”) relationship, which suggests that a digitizedOCT signal, while commonly sampled uniformly in time, is non-uniformlydistributed in wavenumber space, or k-space. Poor or imprecisecalibration could significantly degrade the system performance in termsof the resolution and the ranging accuracy, as well as other parameters.One study reported a hardware-based calibration by clocking the A/Dconverter with an uneven sampling in time to compensate for thenon-linear sweeping operation. This can reduce the time consumption ofsoftware calibration, but increases the overall cost as the electronicsare more complex, and is not feasible for different operationfrequencies of the source. Similarly, a broadband source can be used andthe frequencies swept, such as with a movable grating or prism. Otherapproaches may employ a wideband source with a tunable filter that scansor selects individual wavelengths. However, the power of any selectedwavelength component is always much lower than the total power, which isa drawback of this approach. Moreover, a complex tuning/scanningmechanism is required for precise and repeatable functioning. Toovercome the low-power limitation with previous approaches, the morecommon approach is to use a wideband source that is placed in anexternal cavity tunable laser as a gain medium, and in which a gratingor prism is used as a tuning mechanism. Even in this more commonapproach, however, the issue of a complex tuning mechanism is present asa drawback.

A nearest neighbor check algorithm is popularly used in current SS-OCTsystems for calibration. Its basic concept is using a sliding windowwith fixed width (e.g., 3 points or 5 points) to select consecutivesubsets in the digitized clock data set, then searching for extrema inthis subset as a final finding. This algorithm needs less computationand is presumably fast for calculation. However, its accuracy issubstantially compromised as it is intrinsically sensitive to noise orphase errors in the calibration signal. Practically, prominent noisecannot be completely eliminated in the calibration signal, which maysubstantially affect the calibration accuracy. In addition, advancedcalibration typically results in an increased processing burden.

Analog-to-digital (“A/D”) conversion is a signal-to-noise ratioperformance limiting step in current systems employed for both SS-OCTand FD-OCT. The basic component to all A/D conversion is the quantizer,whose output is always the closest discrete level to the analog input.The interval between the discrete levels is usually uniform, whichdetermines the quantization noise. Thus, the maximum SNR of a given A/Dconverter is limited by the total of these discrete reference levels.Any input signal with a higher SNR than that of the converter willinevitably suffer a signal loss in the stage of A/D conversion. Thedetection parameters of SS-OCT and FD-OCT appear to be inferior toTD-OCT, contrary to many current opinions. This concern may not be apractical issue for OCT imaging in transparent materials such as humaneyes or certain plastics, which have low dynamic range. However, theconcern could limit the capability of these techniques to penetrate manynon-transparent materials, semi-transparent materials, non-biologicalmaterials, or layered or thick samples thereof without improvedperformance characteristics, including a larger dynamic range andimproved SNR

In light of the foregoing, it would therefore be desirable to provide amore effective SS-OCT calibration system and method that compensate fornonlinearities resulting from vector space conversion andnon-repeatability and instability in source sweeping. In doing so, itwould be desirable to provide such a method that is more accurate andreliable than those previously existing methods. It would also bedesirable to provide a system and method for spectral domain OCT thatexhibits a larger dynamic range and improved SNR.

SUMMARY OF THE INVENTION

The present invention overcomes the aforementioned drawbacks byproviding a system and method for performing real-time calibration ofsignal information acquired by spectral domain optical coherencetomography (“OCT”). In addition. A search algorithm for cross-points,peak points, and trough points in the calibration signal is provided by,for example, a genetic algorithm (“GA”). Using the calibration signaland the estimated extrema, a series of more accurate, or “calibration,”extrema are subsequently calculated by an interpolation method, such asa cubic spline interpolation. Similarly, using the calibration signaland the estimated crossing points, a series of more accurate, or“calibration,” crossing points are calculated using a curve fittingmethod, such as a linear interpolation. The acquired image or A-scandata, which is conventionally in the form of an interference signal, isthen calibrated using these calculated series of calibration extrema orcrossing points.

It is an aspect of the invention to provide an optical coherencetomography system that includes a light source, an interferometer inoptical communication with a sample and the light source and configuredto receive input light therefrom, and a detector in opticalcommunication with the interferometer and configured to receive outputlight therefrom. The system may also include a logarithmic amplifier incommunication with the light source and configured to receive andamplify therefrom a calibration signal. The optical coherence tomographysystem further includes a processor coupled to the detector, the lightsource, the processor being configured to receive a signal from thedetector; determine, from the received signal, an interference signalindicative of interference patterns in the output light; receive thecalibration signal; identify a series of extrema and a series ofcrossing values in the received calibration signal; identify a series ofcalibration extrema from the identified series of extrema and receivedcalibration signal by performing a first interpolation; identify aseries of calibration crossing values from the identified series ofcrossing values and received calibration signal by performing a secondinterpolation; calibrate the interference signal using the using theidentified series of calibration extrema and series of calibrationcrossing values; and reconstruct an image of the sample from therecalibrated interference signal. The system may also include alogarithmic amplifier in communication with the detector for amplifyingthe interference signal so that its dynamic range is increased.

It is another aspect of the invention to provide an optical coherencetomography system that includes a light source, a detector, and aninterferometer in optical communication with the light source and thedetector. A logarithmic amplifier is provided to be in communicationwith the light source and configured to receive and amplify acalibration signal therefrom. A processor is provided to be incommunication with the logarithmic amplifier and the interferometer, andthe processor is configured to receive a spectral interference signalfrom the detector; receive the amplified calibration signal from thelogarithmic amplifier; calibrate the received spectral interferencesignal using the received amplified calibration signal; and produce animage having an increased dynamic range from the calibrated spectralinterference signal.

It is yet another aspect of the invention to provide a method forproducing an image of a subject with an OCT system. At least one of areference path and a sample path, which is in optical communication withthe subject, of the OCT system are illuminated with a light source. Aninterference signal is then identified from the reference and samplepaths of the OCT system, and a calibration signal acquired from lightemitted by the light source. The calibration signal may be amplifiedwith a logarithmic amplifier to produce an amplified calibration signalthat is more robust to phase errors and to fluctuations in the originalcalibration signal. A series of extrema and a series of crossing valuesare then estimated from the acquired calibration signal. From thesevalues and the calibration signal, a first and second series,respectively, of calibration characteristics are identified using,respectively, a first and second interpolation. The interference signalis then calibrated using at least one of the identified first and secondseries of calibration characteristics and an image of the subjectreconstructed using the calibrated interference signal. The interferencesignal may optionally be logarithmically amplified prior to ananalog-to-digital conversion to increase its dynamic range afteranalog-to-digital conversion.

It is yet another aspect of the invention to provide a method forproducing an image of a subject with an optical coherence tomography(OCT) system. At least one of a reference path of the OCT system and asample path of the OCT system, the latter which is in opticalcommunication with a subject, is illuminated with a light source. Aninterference signal is identified from the reference and sample paths ofthe OCT system, and a calibration signal is acquired from light emittedby the light source. At least one characteristic of the calibrationsignal is identified, and a first series of calibration characteristicsis identified from the at least one characteristic of acquiredcalibration signal by performing a first interpolation. Additionally, asecond series of calibration characteristics is identified from the atleast one characteristic of acquired calibration signal by performing asecond interpolation. The interference signal is then calibrated usingthe first and second series of calibration characteristics, and an imageof the subject reconstructed using the calibrated interference signal.

The foregoing and other aspects and advantages of the invention willappear from the following description. In the description, reference ismade to the accompanying drawings which form a part hereof, and in whichthere is shown by way of illustration a preferred embodiment of theinvention. Such embodiment does not necessarily represent the full scopeof the invention, however, and reference is made therefore to the claimsand herein for interpreting the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graphic representation of an exemplary free-space Michelsoninterferometer;

FIG. 2 is a block diagram of an exemplary swept-source optical coherencetomography (“SS-OCT”) system employed when practicing some embodimentsof the present invention;

FIG. 3 is a graphic representation of an exemplary calibration signal,or frequency clock signal, produced by a Mach-Zehnder interferometer;

FIG. 4 is a flowchart setting for the steps of an exemplary method forcalibration and image reconstruction employed by the OCT system of FIG.2;

FIG. 5 is a block diagram of an exemplary SS-OCT system that provides alogarithmic amplification of a calibration signal for improvedcalibration performance;

FIG. 6 is a flowchart setting for the steps of an exemplary method forcalibration and image reconstruction employed by the OCT system of FIG.5;

FIG. 7A is a block diagram of an exemplary SS-OCT system that provides alogarithmic amplification of a spectral interference signal for improveddynamic range;

FIG. 7B is a block diagram of the detection system employed in theexemplary SS-OCT system of FIG. 7A;

FIG. 8 is a block diagram of an exemplary SS-OCT system that provides alogarithmic amplification of a spectral interference signal for improveddynamic range and of a calibration signal for improved calibrationperformance; and

FIG. 9 is a block diagram of an exemplary SS-OCT system that provides anadjustable reference arm mirror in combination with variable band-passfiltering of the spectral interference signal for improvedsignal-to-noise ratio of the spectral interference signal.

DETAILED DESCRIPTION OF THE INVENTION

The theoretical analysis of a spectral-domain (“SD”) optical coherencetomography (“OCT”) system, such as a swept-source OCT (“SS-OCT”) orFourier domain OCT (“FD-OCT”) system, is based, for example, on afree-space Michelson interferometer. This simplification generally holdsregardless of the differences in interferogram measurement or whetherthe system is configured in free space or fiber-optically, and whether adifferent interferometer is employed. While reference is made herein toOCT systems and methods, it will be appreciated by those skilled in theart that the systems and methods are also applicable for low coherenceinterferometry.

An exemplary configuration of a free-space Michelson interferometer 100is depicted in FIG. 1, to which reference is now made. A coupler 102that also acts as a beam splitter, such as a 50:50 beam splitter,divides a light beam 104 from a light source 106 into a reference arm108 and a sample arm 110 of the interferometer 100. In the reference arm108, the light beam 104 is returned by a mirror 112 with amplitudereflectivity, r_(R). The light beam 104 in the sample arm 110 isprojected onto a sample 114, usually being focused to provide a desiredlateral resolution. Exemplary samples 114 include biological tissueswhether in vivo or in vitro. Fresnel reflections occur at anydiscontinuities of refractive index within the sample 114. Thesereflected waves carry information about the microstructures of thesample 114, and are collected and returned to the coupler 102. Bothreturned beams are combined at the coupler 102, thereby generating aninterferogram at the exit 116 of the interferometer 100. To furthersimplify this theoretical analysis, it is assumed that there are noinsertion losses, or dispersion or polarization effects in the opticalpaths; however, it is noted that these assumptions do not detract fromthe broad applicability of the systems and methods described herein.

The incident light field at the coupler 102 is typically classicallydescribed as a complex function whose real part represents the reallight disturbance, and is conjugated with the imaginary part through aHilbert transform as follows:

E ₀(t)=∫₀ ^(∞) a ₀(ν)e ^(i(φ) ⁰ ^((ν)−2πνt)) dν  (1);

where a₀(ν) and φ₀(ν) represents the real-value amplitude and phasespectrum of the incident light, respectively, and ν is the frequency ofthe light. Thus, the intensity of this light beam is represented by:

$\begin{matrix}{{I_{0} = {{\frac{1}{2}{\langle{{E_{0}(t)}{E_{0}^{*}(t)}}\rangle}} = {{\int_{- \infty}^{\infty}{{S(v)}{v}}} = {2{\int_{0}^{\infty}{{S(v)}{v}}}}}}};} & (2)\end{matrix}$

where S(ν) represents the power spectrum. According to Wiener-Khinchintheorem, the autocorrelation function, Γ₀(t), of the incident light beamis the inverse Fourier transform of the power spectrum, S(ν):

Γ₀(t)=∫_(−∞) ^(∞) S(ν)e ^(i2πνt) dν  (3).

This autocorrelation function is a real real-value function of time, t,considering the symmetry between the positive-frequency part and thenegative-frequency part of the power spectrum, S(ν). In practice, themeasured or generated light spectrum spans the positive frequency rangein accordance with the form of 2·S(ν).

Referring still to FIG. 1, for SD-OCT techniques, the mirror 112 in thereference arm 108 is generally in a static position for a giveninterferogram generation. Thus, a spectral interferogram is measuredeither by placing a spectrometer at the exit 116 of the interferometer100, or by sweeping out the spectrum, S(k), as a function of wavenumber,k, in time. The former approach is usually referred as Fourier domainOCT, and the latter as swept-source OCT. Accordingly, the individualspectral components of the light field from both the reference arm 108and the sample arm 110 can be respectively described as:

$\begin{matrix}{{{E_{R}( {t,k} )} = {\frac{1}{2}r_{R}{a_{0}(k)}^{{\varphi}_{0}{(k)}}^{{2\pi}\; {vt}}{\int_{- \infty}^{\infty}{^{{- {2\pi}}\; {kz}_{R}}\ {z}}}}};} & (4) \\{{{E_{S}( {t,k} )} = {\frac{1}{2}{a_{0}(k)}^{{\varphi}_{0}{(k)}}^{{2\pi}\; {vt}}{\int_{- \infty}^{\infty}{{r_{S}(z)}^{{- {2\pi}}\; {kz}}\mspace{11mu} {z}}}}};} & (5)\end{matrix}$

where the phase term in the integral of Eqn. (4) is introduced by thereference mirror 112 being position a distance, z_(R), away from thecoupler 102; the coefficient, r_(R)/2, indicates that the amplitudereflectivity of the mirror 112 is set as r_(R); and the light beam 104is split twice by the coupler 102. Similarly, in Eqn. (5), the termr_(S)(z) represents the backscattering potential of sample 114, and isassumed to be independent of the wavelength, λ. The variable, z, is adistance measured from the coupler 102 to a given backscatter, and theintegral over z reflects all the contributions to the returned samplebeam from the scattering potential. When the backscatter is a singlebackscatter event, the distance, z, is an optical distance. Theintensity of each spectral component at the exit 116 of theinterferometer is:

$\begin{matrix}\begin{matrix}{{I_{D}(k)} = {\frac{1}{2}{\langle{( {{E_{R}( {t,k} )} + {E_{S}( {t,k} )}} ) \cdot ( {{E_{R}( {t,k} )} + {E_{S}( {t,k} )}} )^{*}}\rangle}}} \\{= {{\frac{1}{2}{\langle{{E_{R}( {t,k} )}{E_{R}^{*}( {t,k} )}}\rangle}} + {\frac{1}{2}{\langle{{E_{S}( {t,k} )} + {E_{S}^{*}( {t,k} )}}\rangle}} +}} \\{{{\frac{1}{2}{\langle{{E_{R}( {t,k} )}{E_{S}^{*}( {t,k} )}}\rangle}} + {\frac{1}{2}{{\langle{{E_{S}( {t,k} )}{E_{R}^{*}( {t,k} )}}\rangle}.}}}}\end{matrix} & (6)\end{matrix}$

Accordingly:

$\begin{matrix}{{{I_{R}(k)} = {{\frac{1}{2}{\langle{{E_{R}( {t,k} )}{E_{R}^{*}( {t,k} )}}\rangle}} = {\frac{1}{4}{S(k)}r_{R}^{2}}}};} & (7) \\{{{I_{S}(k)} = {{\frac{1}{2}{\langle{{E_{S}( {t,k} )}{E_{S}^{*}( {t,k} )}}\rangle}} = {\frac{1}{4}{{S(k)} \cdot {{{FT}\{ {r_{S}(z)} \}}}^{2}}}}};} & (8)\end{matrix}$

and where the remainder of Eqn. (6) can be given by,

$\begin{matrix}{{{{\frac{1}{2}{\langle{{E_{R}( {t,k} )}{E_{S}^{*}( {t,k} )}}\rangle}} + {\frac{1}{2}{\langle{{E_{S}( {t,k} )} + {E_{R}^{*}( {t,k} )}}\rangle}}} = {\frac{1}{4}{S(k)}{r_{R} \cdot ( {{{FT}\{ {r_{S}( {z - z_{R}} )} \}} + {{FT}\{ {r_{S}( {z_{R} - z} )} \}}} )}}};} & (9)\end{matrix}$

where FT{. . .} in Eqns. (7)-(9) indicates the Fourier transformoperation. Substituting Eqns. (7)-(9) into Eqn. (6), the spectralinterferogram at the exit 116 of the interferometer can be described as:

$\begin{matrix}{{I_{D}(k)} = {\frac{1}{4}{{S(k)} \cdot {\begin{bmatrix}{r_{R}^{2} + {r_{R}( {{{FT}\{ {r_{S}( {z - z_{R}} )} \}} + {{FT}\{ {r_{S}( {z_{R} - z} )} \}}} )} +} \\{{{FT}\{ {r_{S}(z)} \}}}^{2}\end{bmatrix}.}}}} & (10)\end{matrix}$

By taking the inverse Fourier transform of the spectral interferogram,I_(D)(k), presented in Eqn. (10), a real-valued function of the singlevariable, z, can be obtained:

$\begin{matrix}{{{{FT}^{- 1}\{ {I_{D}(k)} \}} = {\frac{1}{4}{FT}^{- 1}{\{ {S(k)} \} \otimes \begin{bmatrix}{{r_{R}^{2}{\delta (z)}} + {r_{R}{r_{S}( {z - z_{R}} )}} + {r_{R}{r_{S}( {z_{R} - z} )}} +} \\{{FT}^{- 1}\{ {{{FT}\{ {r_{S}(z)} \}}}^{2} \}}\end{bmatrix}}}};} & (11)\end{matrix}$

where “

” indicates the convolution operation and δ(z) is the Dirac deltafunction. Following again from the Wiener-Khinchin theorem, the lastterm on the right side of Eqn. (11), FT⁻¹{|FT{r_(S)(z)}|²}, isessentially and adequately equivalent to the autocorrelation of thebackscattering sample potential, r_(S)(z), which presents mainly aroundz=0. The inverse Fourier transform of the spectrum is theautocorrelation function, Γ₀(z), in z-space, which is convolved with thefour terms in the brackets.

If the mirror 112 position, z_(R), in the reference arm 108 is offsetfrom the sample 114, that is, if the optical path lengths in both armsdiffer by an appropriate amount, the third and fourth terms in Eqn.(11), r_(R)r_(S)(z−z_(R)) and r_(R)r_(S)(z_(R)−z), respectively, can bedistinguished from the other terms, such as the delta function, δ(z), atz=0, and the autocorrelation term of the symmetric backscatteringpotential around z=0. These third and fourth terms, r_(R)r_(S)(z−z_(R))and r_(R)r_(S)(z_(R)−z), respectively, relate to the scatteringpotential, and are designated to be retrieved.

On the other hand, manipulation of the optical path length in the samplearm 110, z, can also be utilized to distinguish the two scatteringpotential terms in Eqn. (11) separate from each other because they aresymmetrical with respect to z=z_(R), thereby allowing isolation of theseterms. It is useful to notice that, practically, the sweeping ormeasurement of the spectrum obtains only the positive wavenumber part ofthe spectral interferogram in Eqn. (10), in the appropriate deviceconfiguration, which means the inverse Fourier transform in Eqn. (11)will generate a complex function. Thus, the modulus is calculated toretrieve r_(S)(z).

Practically, in SS-OCT, the spectrum is swept in the time domain, whichmeans the acquired spectral interferogram of the detector is intended toperform linearly in the time domain. Thus, the intensity, I_(D)(t), is afunction of time instead of the wavenumber. Because of this, theintensity, I_(D)(t), must be transformed into wavenumber space, ork-space, before performing the inverse Fourier transform in Eqn. (11).Therefore, the relationships between the wavenumber, k, and the sweepingtime, t, in terms of a function k=f(t) must be taken into account. Usingthe wavenumber-time relationship, the interferogram in k-space can beobtained as I_(D)(f⁻¹(k)). This process is generally referred as“calibration” in SD-OCT.

Given a strict linear relationship between k and t, as follows:

$\begin{matrix}{{k = {{\frac{\Delta \; k}{\Delta \; t}t} + k_{0}}};} & (12)\end{matrix}$

where Δt is the sampling window in the time domain; Δk is the wavenumberrange in the time interval Δt ; Δk/Δt represents the constant sweepingspeed; k₀ is the center wavenumber; and t ranges from −Δt/2 to Δt/2, thetransformed k-space interferogram is given by:

$\begin{matrix}{{I_{D}(k)} = {\frac{1}{4}{{S( {\frac{\Delta \; T}{\Delta \; k}( {k - k_{0}} )} )} \cdot {\begin{bmatrix}{r_{R}^{2} +} \\{{r_{R}( {{{FT}\{ {{r_{S}z} - z_{R}} \}} + {{FT}\{ {r_{S}( {z_{R} - z} )} \}}} )} +} \\{{{FT}\{ {r_{S}(z)} \}}}^{2}\end{bmatrix}.}}}} & (13)\end{matrix}$

The inverse Fourier transform on this converted interferogram, thus,becomes:

$\begin{matrix}{{{{FT}^{- 1}\{ {I_{D}(k)} \}} \propto {{\Gamma_{0}( {\frac{\Delta \; k}{\Delta \; T}z} )} \otimes \begin{bmatrix}{{r_{R}^{2}{\delta ( {\frac{\Delta \; k}{\Delta \; T}z} )}} +} \\{{r_{R}r_{S}\frac{\Delta \; k}{\Delta \; T}( {z - z_{R}} )} +} \\{{r_{R}r_{S}\frac{\Delta \; k}{\Delta \; T}( {z_{R} - z} )} +} \\{{FT}^{- 1}\{ {{{FT}\{ {r_{S}( {\frac{\Delta \; k}{\Delta \; T}z} )} \}}}^{2} \}}\end{bmatrix}}};} & (14)\end{matrix}$

which indicates that, for such a linear relationship as the one in Eqn.(12), the inverse Fourier transform can be directly applied on I_(D)(t).Consequently, the designated profile can then be retrieved by rescalingthe data in the z-dimension. However, many kinds of sophisticated sweptlaser sources can provide relationships that approach linearity, to somedegree, between the wavelength, λ, and time, t, such as:

$\begin{matrix}{{\lambda = {{\frac{\Delta\lambda}{\Delta \; T}t} + \lambda_{0}}};} & (15)\end{matrix}$

where Δλ/Δt represents the constant wavelength sweeping speed; λ₀ is thecentral wavelength; and t ranges from −Δt/2 to Δt/2. This linearity inwavelength, λ, indicates a nonlinearity between k and t because:

$\begin{matrix}{t = {{\frac{\Delta \; T}{\Delta\lambda}( {\lambda - \lambda_{0}} )} = {\frac{\Delta \; T}{\Delta\lambda}{( {\frac{1}{k} - \frac{1}{k_{0}}} ).}}}} & (16)\end{matrix}$

Expanding the term in the parenthesis into its power series around k₀,Eqn. (16) becomes:

$\begin{matrix}{t = {{\frac{\Delta \; T}{\Delta\lambda}\lbrack {{{- \frac{1}{k_{0}}}( {\frac{k}{k_{0}} - 1} )} + {\frac{1}{k_{0}}( {\frac{k}{k_{0}} - 1} )^{2}} + {\frac{1}{k_{0}}( {\frac{k}{k_{0}} - 1} )^{3}} + \ldots}\mspace{14mu} \rbrack}.}} & (17)\end{matrix}$

Eqn. (17) indicates that this nonlinearity, which is frequently referredto as an issue of non-uniform sampling, will introduce a series ofnonlinear terms in the converted spectral interferogram in k-space.These nonlinearities cause distortions in the autocorrelation Γ₀(z), anddiminish the spatial resolution and ranging accuracy of the SS-OCTsystem. If a priori knowledge of the nonlinearities exists and isemployed, the calibration becomes necessary to perform only before eachOCT operation. Unfortunately, such a priori information is not commonlyknown for many laser sweeping mechanisms, particularly with respect tothe stability and repeatability of the spectrum sweeping. For example, acommon mechanism of irregularities in SS-OCT results from using a leadzirconate titanate (“PZT”) resonator in the tuning mechanism. Thehysteresis of the PZT affects the repeatability and linearity of thespectrum. In addition, stability errors can be caused a variety ofsources, such as jitter noise in the PZT resonator driving signals.Thus, a real-time calibration is highly desirable and demanded.

In an exemplary SS-OCT system employed when practicing the presentinvention, a Mach-Zehnder interferometer (“MZI”) is used for thereal-time calibration and compensation purposes. It will be appreciatedby those skilled in the art, however, that other interferometers mayalso be used to produce a calibration signal as described herein. An MZIis one configuration of a two-beam interferometer. The intensity of theMZI output periodically changes if the wavelength of the monochromaticor quasi-monochromatic light source at the input is scanning. Thisoutput signal contains maxima and minima that are equally spaced in theoptical frequency domain, or equivalently, the wavenumber domain(“k-space”). The difference between two maxima is defined by the freespectral range (“FSR”) of the interferometer, which is determined by theoptical-path-length-mismatch between both arms in the MZI. An exemplaryFSR is set at around 100 GHz, which corresponds to a wavenumber intervalof around 3.33 per centimeters (“cm⁻¹”). Zero-crossings in theelectronic output signal of the MZI are also used, as described below.In an SS-OCT system, the wavelength of the laser source is rapidlytuned. As the extrema and crossing-points are determined in a temporalsequence, they are used to index the dataset of the simultaneouslycaptured spectral interferogram. Thus, the OCT signal is transformedinto a set of data with a fixed wavenumber interval before fast Fouriertransform processing.

The general optical arrangement of an exemplary high speed SS-OCT system200 is depicted in FIG. 2. Such an exemplary SS-OCT system 200 includesa fiber optic Michelson interferometer as a central component of thesystem architecture. It will be readily appreciated by those skilled inthe art, however, that the succeeding discussion is directed to only oneof many different possible configurations of such an SS-OCT system. Alight source 202, such as a swept laser source, provides, for example,100 nanometer (“nm”) full-width half-maximum (“FWHM”) wavelength scanrange at, for example, a central wavelength of 1325 nm, as well as 10 mWoutput power. Those skilled in the art will appreciate that light sourceparameters, such as the central wavelength, can be changed depending onthe particular application at hand, the particular imaging needs, orgiven availability. The wavelength sweeping rate is, for example, 16kHz, and the instantaneous coherence length of the laser is measured tobe, for example, greater than 7 mm.

In such a light source 202, a Mach-Zehnder interferometer is embedded toprovide a frequency clock with, for example, 100 GHz optical frequencyspace (around 0.6 nm in wavelength). An analog calibration signal isoutputted from the MZI in the light source 202 along line 204. Thiscalibration signal is utilized for real-time spectrum calibration in theSS-OCT system 200.

The light beam produced by the light source 202 is guided into acirculator 206 and an optical fiber coupler 208, such as a 2×2 50:50fiber coupler. The two output ports of the optical fiber coupler 208compose the two arms of the Michelson interferometer. One arm referredto as the reference arm, is projected by a fiber collimator 210 througha lens 212 into a mirror 214, which is movable along the beam directionthrough a micro-stage. In an exemplary configuration of the referencearm, a motorized Lefevre type polarization controller 216 may be builtand implemented for polarization measurement or control with the SS-OCTsystem 200. The polarization controller 216 may be controlled by a stepmotor 218 to change the polarization of the light beam in the referencearm. For a Lefevre polarization controller, the step motor 218 changes,for example, the diameters of the optical fiber loops in thepolarization controller 216, thereby changing the polarization of thelight transmitted through the polarization controller 216. It will beappreciated by those skilled in the art that polarization controllersother than Lefevre type controllers can also be implemented. Forexample, the polarization may be controlled by way of the addition andremoval of wave plates, such as quarter-wave plates or half-wave plates,in the reference arm. Additionally, fiber-based polarization controllersother than Lefevre polarization controllers can be implemented, such asthose that operate by compressing an optical fiber to induce a variablebirefringence in the optical fiber. It will also be appreciated by thoseskilled in the art that the intensity of the light beam in the referencearm may also be changed by the polarization controller 216 by way ofchanging the polarization of the light beam in the reference arm.

The second arm, referred to as the sample arm, is projected by a fibercollimator 220 through a lens 222 onto an X-Y scanner 224. The scannedbeam is then focused on a sample 226 through an objective lens 228having, for example, a 30 mm focal length. The X-Y scanner 224 issynchronized with the light source sweeping so that so-called B-scanningand third-dimension scanning is provided for OCT imaging.Three-dimensional imaging is provided, for example, by adding multipleB-scans together.

The light beams returning from the reference and sample arms combine andinterfere at the optical fiber coupler 208, thereby producinginterferograms. These interferograms are provided from two ports of theoptical fiber coupler 208 and guided into a the circulator 206 and asecond coupler 230. This second coupler 230 has, for example, 95:5splitting ratio and also helps to guide a beam from a guiding laser 232to both the reference and sample arms. The interferograms from thecirculator 206 and second coupler 230 are provided to detectors 234, 236before passing to a dual-balanced detector 238.

The digital spectral interference and calibration signals are providedfrom the A/D converter 242 to a processor 246 for calibration, imagegeneration, and other processing tasks. The processor 246 may include,for example, capabilities for parallel and synchronous acquisition oftwo channels for recording the spectral interference signal from thedual-balanced detector and the calibration signal from the MZI bycontrolling and communication with the A/D converter 242. The controlsignal for the X-Y scanner and the system synchronization are generatedthrough a digital-to-analog (“D/A”) converter 248, and are subsequentlysupplied to the appropriate components of the SS-OCT system 200.

The calibration signal from the MZI is substantially evenly sampled bythe A/D converter 242 simultaneously along with the spectralinterference signal from the dual-balanced detector 238. However, inother configurations that calibration signal from the MZI can beprovided directly to and sampled at the processor 246, thereby bypassingthe A/D converter 242. An exemplary calibration signal is illustrated inFIG. 3. As described earlier, the calibration signal is used as areference with its cycles being substantially equidistant in frequency.The difference between two maxima is defined by the FSR of the MZI.

In one previous study, recalibration was performed using a fast nearestneighbor check algorithm, which is referred as the regular calibrationhere. A fast search algorithm for peak points and trough points in thecalibration signal was performed. If the samples had satisfied theconditions of the algorithm, the corresponding points in the OCT signalwere added to the recalibrated signal array. While this method providesspeed that is adequate for real-time preview, it fails to determine theactual peaks and troughs and leads to errors or incomplete corrections.

In some embodiments, a genetic algorithm (“GA”) is employed to optimizethe search method in the calibration trace. An appropriate fitnessfunction is defined in a way that local extremes and vicinity to zeroincrease the fitness value for extremes (peaks and troughs) and crosspoints, respectively. The value of the Gaussian envelope of thecalibration signal in proximity of each extreme is used as an auxiliarytool for the fitness function. Using this dataset as the firstgeneration, during each successive generation, a number of points areselected based on their quality measured by fitness function.Consecutive iterations of this method increase the average fitness ofthe population of the next generation. It is noted that multiplegenerations are achieved in microseconds. This generational processcontinues, until the requisite number of points with desired quality isattained. At this point the algorithm is terminated. These points are,afterwards, used for interpolation.

In order to find the actual extremes and cross points, twointerpolations are performed on the obtained data; however, it should beappreciated by those skilled in the art that more than twointerpolations could also be performed, or, alternatively, at least oneinterpolation and at least one curve fitting method can also beemployed. Cubic spline interpolation is performed for the extremes andinterference signal, while linear interpolation is done for thecross-points. The functions used here for extremes and interferencesignal must behave smoothly to avoid the jitter noise. To satisfy thiscondition, the functions must be differentiable and their secondderivative must be continuous. Considering this fact and also tominimize the interpolation error and avoid Runge's phenomenon, splinefunctions are used here that normally satisfy these requirements. Inthis example, it should be noted that the samples are acquired at a ratethat guarantees that there is substantially only one extremum in eachinterpolation. However, with more complex approaches, more than oneextremum may occur in each interpolation.

Real-time display requires a fast recalibration algorithm. Usingmulti-threading technique, inverse Fourier transform, GA, andinterpolation are performed in parallel for the axial scans, andtherefore they do not increase the overall time of the process. Thismethod increases the performance of the system in different ways. First,adding cross points to the reference points leads to doubled samplingfrequency and higher accuracy in signal reconstruction. Second, the GAbased optimized search and precise interpolation minimizes the errors infinding the reference points, both by reducing nonlinearities from thesource and the A/D conversion process during t-to-k space conversion.Image resolution, dynamic range, and image quality are improved by usingthe proposed method in a SS-OCT system.

Referring now to FIG. 4, the steps of an exemplary method forreconstructing an image from a calibrated spectral interference signalacquired with, for example, the SS-OCT system of FIG. 2 are illustrated.First, image data is acquired in the form of interference patterns fromthe reference and sample paths of the OCT system, as indicated at step400. A calibration signal is similarly provided, as indicated at step402. For example, and MZI is coupled to the light source of the OCTsystem, and as a wavelength of the light produced therefrom is sweptover a range of values, a calibration signal is produced by the MZIsubstantially contemporaneous with the acquisition of the image data.

The calibration signal is sampled by an A/D converter to produce adigital representation of the calibration signal that is utilized forprocessing, as indicated at step 404. In alternative configurations,however, the calibration signal may be sampled directly at theprocessor. From the digitized calibration signal, estimates of theextrema and crossing points in the calibration signal are produced, asindicated at step 406. These crossing points may be zero-crossingpoints, DC-crossing points, or other crossing points. As discussedabove, the estimation process is performed by searching for the extremaand crossing points with a global optimization method, such as a geneticalgorithm (“GA”).

Using the calibration signal and the estimated extrema, more accurateextrema are calculated next, as indicated at step 408. This is achieved,for example, by performing a cubic spline interpolation. Likewise, moreaccurate crossing points are calculated at step 410 using thecalibration signal and estimated crossing points. This is achieved, forexample, by performing a linear interpolation. The calculated extremaand crossing points are distributed substantially uniformly across anabscissa that represents, for example, either wavelength or wavenumber.These points and their substantially uniform distribution aresubsequently utilized to calibrate the acquired image data, as indicatedat step 412.

Since the calibration signal was originally produced substantiallycontemporaneously with the acquisition of the image data, thecalibration is achieved by forming a so-called calibrated signal array.Such a calibrated signal array is formed by selecting those values inthe acquired image data that are associated with the wavelength orwavenumber values corresponding to the calculated extrema and crossingpoints. In this manner, the image data is calibrated such that there isa substantially linear relationship between either the wavelength orwavenumber of the acquired image data and the progression of time duringwhich the data was acquired. Using this calibrated signal array, animage of the subject is reconstructed as indicated at step 414.

In some configurations of an SS-OCT system, such as the one illustratedin FIG. 5, the calibration signal on line 204 is additionally amplifiedby a true logarithmic amplifier 244. Subsequently, this amplifiedcalibration signal is supplied to the A/D converter 240. Theamplification of the calibration signal results in a significantimprovement in the calibration of the spectral interference signal byimproving the searching accuracy for extrema and crossing-points in thecalibration signal. The reason for this improvement is two fold. First,a logarithmically-amplified calibration signal is less sensitive tophase errors than a regular calibration signal, and, second, thesignal-to-noise ratio (“SNR”) of the true logarithmic amplifier 244output is higher than its input when the input SNR is at or above one.Thus, the logarithmically-amplified calibration signal will have lessfluctuation at extreme regions, thereby significantly improving λ-spaceto k-space calibration accuracy, as well as the accuracy of thosecalibration techniques where other vector space conversions are used.The logarithmic amplification of the calibration signal also compensatesfor nonlinearities of the source sweep.

Referring now to FIG. 6, the steps of an exemplary method forreconstructing an image from a calibrated spectral interference signalacquired with, for example, the SS-OCT system of FIG. 5 are illustrated.First, image data is acquired in the form of interference patterns fromthe reference and sample paths of the OCT system, as indicated at step600. A calibration signal is similarly provided, as indicated at step602. For example, an MZI is coupled to the light source of the OCTsystem, and as a wavelength of the light produced therefrom is sweptover a range of values, a calibration signal is produced by the MZI.This calibration signal is produced substantially contemporaneous withthe acquisition of the image data. As described above, this calibrationsignal is amplified by a true logarithmic amplifier so that the extremaand crossing values therein can be more readily identified during thecalibration procedure.

After amplification, the calibration signal is sampled by an A/Dconverter to produce a digital representation of the amplifiedcalibration signal that is utilized for processing, as indicated at step604. In alternative configurations, the calibration signal may bedirectly sampled at the processor. From the digitized calibrationsignal, estimates of the extrema and crossing points in the calibrationsignal are produced, as indicated at step 606. These crossing points maybe zero-crossing points, DC-crossing points, or other crossing points.As discussed above, the estimation process is performed by searching forthe extrema and crossing points with a global optimization method, suchas a genetic algorithm (“GA”).

Using the calibration signal and the estimated extrema, more accurateextrema are calculated next, as indicated at step 608. This is achieved,for example, by performing a cubic spline interpolation. Likewise, moreaccurate crossing points are calculated at step 610 using thecalibration signal and estimated crossing points. This is achieved, forexample, by performing a linear interpolation. These points and theirsubstantially uniform distribution are subsequently utilized tocalibrate the acquired image data, as indicated at step 612.

Since the calibration signal was originally produced substantiallycontemporaneously with the acquisition of the image data, thecalibration is achieved by forming a so-called calibrated signal dataarray. Such a calibrated signal data array is formed by selecting thosevalues in the acquired image data that associated with the calculatedextrema and crossing points. In this manner, the image data iscalibrated such that there is a substantially linear relationshipbetween either the wavelength or wavenumber of the acquired image dataand the progression of time during which the data was acquired. Usingthis calibrated signal array, an image of the subject is reconstructedas indicated at step 614.

By way of example, one definition of the dynamic range of an OCT systemis herein defined as the ratio of the maximum detectable reflectionsignal, i_(max), and the minimum detectable reflection signal, i_(min),after digitization. Dynamic range is a dimensionless parameter thatcharacterizes the intra-A-scan measurement capability of OCT. Thiscapability is important for OCT in the circumstances of imaging tissuesand materials that are not transparent, where the reflections from thedeep areas of the tissue are substantially lower while other signals,such as the reflections from the surface, can be high enough to saturatein the system. This capability is also important for OCT with respect toseparating different intensities for image contrast. By the foregoingdefinition, the maximum signal, i_(max), could be determined by themaximum detectable reflectivity, r_(S,max), without saturation in theOCT. The minimum signal, i_(min), is usually chosen as same as thesensitivity of the system, which is equivalent to the root-mean-squareintensity of the input-referred noise, σ_(n). These noise sourcesinclude contributions from both the photon and electron noise sources.The dynamic range can be expressed as:

$\begin{matrix}{{DR} = {\frac{i_{\max}}{i_{\min}} = {\frac{i_{\max}(0)}{\sigma_{n}} = {\frac{r_{R}r_{S,\max}I_{0}}{2\sigma_{n}}.}}}} & (18)\end{matrix}$

According to the Parseval's theorem and its counterpart for digitalsignal processing, the energy theorem, the Fourier transform on anysignal and noise would not provide any signal to noise ratioimprovements. Thus, ideally the dynamic range of either the SS-OCT orthe FD-OCT should be identical to the one of TD-OCT. However, this isnot true when reducing the theory to practice. By conducting the Fouriertransform on a spectral interferogram acquired by TD-OCT and applyingWiener-Khinchin theorem, the dynamic range expression of the SD-OCT willbe the same as Eqn. (18) if the equivalent noise source and componentlimitations in each embodiment are the same. Practically, this principleis not applicable for several reasons. First, as discussed above, TD-OCTis intrinsically a noise-matching filtering system, but SS-OCT andFD-OCT are not. Additional noise sources, such as 1/f and thermal noisein SS-OCT, reduce the dynamic range of SS-OCT as the total noiseintensity, σ_(n), increases in Eqn. (18), as discussed below in detail.Second, as shown in FIGS. 4A and 4B, analog-to-digital (“A/D”)conversion is a performance limiting step in current embodiments of bothSS-OCT and FD-OCT, where logarithmic handling of the signal does notoccur prior to the conversion as with TD-OCT. The basic component to allA/D conversion is the quantizer, whose output is always the closestdiscrete level to the analog input. The interval Δ between the discretelevels is usually uniform, which determines the quantization noise whoseroot-mean-square intensity is proportional to Δ. The maximum level ofthe quantizer is 2^(l)Δ, where l is the bit depth of the ADC. Thus, itis contemplated that the dynamic range of SS-OCT and FD-OCT, as acascaded system, is inevitably limited by the ADC, which can beexpressed as:

$\begin{matrix}{{DR}_{{ADC} - {limited}} = {\frac{r_{R}r_{S,\max}2^{l}\Delta}{2\Delta} = {r_{R}r_{S,\max}{2^{l - 1}.}}}} & (19)\end{matrix}$

Because 0≦r_(R) and r_(S,max)≦1, the maximum dynamic range of anADC-limited OCT system may be as small as 2^(l−1). For a 14-bit ADC,this is only about 8096. In FD-OCT, an additional limitation to thedynamic range might arise from the dynamic range of the detector array,which is defined as the ratio of well capacity of the each element andcorresponding readout noise. This process is analogous to the digitizerin the ADC, but each discrete level is actually an electron. Thus,according to Eqn. (19), the detector-array-limited dynamic range can bedescribed as:

$\begin{matrix}{{{DR}_{{Array} - {limited}} = \frac{r_{R}r_{S,\max}Q_{W}}{2\sigma_{n}}};} & (20)\end{matrix}$

where Q_(W) represents the well capacity of individual pixels and σ_(n)represents the prevailing readout noise. For example, if the wellcapacity of a detector array is 17000 electrons/pixel and the equivalentnoise is around 20 electrons/pixel, the dynamic range could be about8500, which is around the dynamic range limited by the ADC. As acascaded system, the dynamic range of the FD-OCT will eventually belimited to either ADC or the detector array, depending on which limitarrives first As the limitations of FD-OCT are considerable comparedwith SS-OCT, most of our efforts here are focused on comparing SS-OCTwith TD-OCT.

With TD-OCT, logarithmic amplification is usually utilized before theADC; thus, the post-digitization dynamic range is approximately 80 dB.With SD-OCT, where a linear signal is applied on the converter, thedynamic range is only 40 dB. This data is in log₁₀ format consistentwith original TD-OCT studies. Recently, however, some investigators haveused a log₂₀ format terminology to represent dynamic range in decibelswithout clarification, giving the impression that the performance isdoubled. Knowing whether dynamic ranges are presented in log₁₀ or log₂₀is critical in evaluating data in this filed, as comparing these twodifferent formats is essentially comparing two different units ofmeasurement

To overcome the aforementioned drawbacks associated with the SD-OCT, atrue logarithmic amplifier (“TLA”) is implemented before the ADC in aSS-OCT, as shown in FIGS. 7A and 7B. A true logarithmic amplifierconverts the amplitude of signal from linear-scale into log-scale. Basedon this nonlinear conversion, the small amplitude components in thesignal are magnified and well preserved. Through the TLA, largeamplitude components will be compressed. By the logarithmicamplification, signals with wide dynamic range can be well preservedafter the A/D conversion, with certain degradations in the resolution oflarge or small signals depending on how parameters are set. An explicitexample is that a signal range from 1-10 volts (9 volts variation) canbe converted into 0−1×C counts after the digitization. However, a signalrange of 10-100 volts (90 volts change) only varies in the same amountof counts (from 1×C−2×C counts). It is noted that C is a constantrepresenting the amplification. Under certain conditions, such astargets with relatively low dynamic range or focus on surfacestructures, it may be of use to allow the system to interchange betweenthe logarithmic and linear amplifiers.

Thus, in some configurations of a SS-OCT system, such as thoseillustrated in FIGS. 7A and 7B, the spectral interference signal fromthe dual-balanced detector 238 is logarithmically amplified by a truelogarithmic amplifier 240, which provides, for example, nominal 90 dBanalog signal and a DC 30 MHz operating bandwidth. The use of the truelogarithmic amplifier 240 allows a significant extension in theachievable dynamic range in SS-OCT, as described above. The amplified,spectral interference signal is subsequently supplied to theanalog-to-digital (“AID”) converter 242. As mentioned earlier, thislogarithmic amplification step provides the SS-OCT system 200 with awider dynamic range than achievable with a conventional SS-OCT systemwithout true logarithmic amplification.

As illustrated in FIG. 8, in some configurations an SS-OCT system mayinclude a logarithmic amplifier 240 between the dual-balanced detector238 and the A/D converter 242 for increasing dynamic range in additionto a logarithmic amplifier 244 on the calibration signal line 204 forimproving the calibration process, as described above in detail.

With reference now to FIG. 9, it is desirable that in someconfigurations of the SS-OCT system, the mirror 214 in the reference armis configured to be adjustably displaced along an axis perpendicular tothe mirror, that is, the “z-axis,” is provided. In addition, a variableband-pass filter 250 is provided between the dual-balanced to detector238 and the A/D converter 242. The variable band-pass filter 250 mayinclude, for example, a single filter whose properties can be altered,or a series of filters that form a filter bank, in which each of thefilters in the series of filters has different properties. Duringoperation of the SS-OCT system when the filter bank is used, differentfilters are selected for their individual properties to vary betweendifferent pass bands.

While logarithmic amplifiers on the calibration signal line 204 orbetween the dual-balanced detector 238 and the A/D converter 242 are notillustrated in FIG. 9, it will be appreciated by those skilled in theart that, as described in detail above, either of these configurationscan be combined with the variable band-pass filter 250 configurationdescribed here. When a logarithmic amplifier is also provided betweenthe dual-balanced detector 238 and A/D converter 242, the amplifier maybe provided before or after the variable band-pass filter 250. Thez-offset provided by the movable mirror 214 is used in connection withthe variable band-pass filter 250 in order to effectively shift theautocorrelation function from an area in the subject into a range wheresubstantially all frequencies are detectable, or where unwantedfrequencies can be readily removed. In this manner, not only isvisualization of the subject enhanced, but factors that deteriorateresolution can be compensated for and complex conjugate ambiguityreduced.

In time domain OCT (“TD-OCT”) systems, the mirror scanning in thereference arm acts to moves the spectrum S(k) to a higher frequency, k₀,which is ultimately determined by the scanning velocity, V. Thus, aband-pass filter is usually implemented to suppress most of the noiseoutside the passband, which offers TD-OCT an optimal signal-to-noiseperformance over the other types of OCT. It is noted that there istypically no Doppler shift or carrier frequencies in SD-OCT techniques.While SS-OCT systems have similar detection electronics as TD-OCTsystems in terms of detector and preamplifier, SS-OCT systems are inmany respects low-pass filtering systems in which some low frequencynoises, such as 1/f noise, including from the detector and amplifier,cannot be easily removed. This indicates that the system is not anoptimal system in terms of signal-to-noise performance.

Different from SS-OCT systems, FD-OCT systems introduce additional noisesources because they capture the signal spectrum, S(k), and noisefluctuations, N(k), with a detector array. Usually a contemporarydetector array, such as a charge-coupled device (“CCD”), which has anon-focal-plane signal integration function, is used. This signalintegration function can be described as a linear summation of thesignal spectrum, S(k), and the noise fluctuations, N(k). Because thesignal spectrum, S(k), adds coherently, whereas the noise fluctuations,N(k), add incoherently, the signal integration function potentiallyoffers signal-to-noise ratio (“SNR”) improvement for FD-OCT. However,like SS-OCT, FD-OCT is also a low-pass filtering system, which is not anoptimal detecting system. In addition, it should be noted that noisesources that are only present in the detector array, such as readout andreset noise, compromise the benefits provided by signal integration.Inevitably, this signal integration function likely decreases thedynamic range of the FD-OCT system.

The band-pass filter and z-offset can be varied separately, similar to,for example, the brightness and contrast adjustments on an ultrasoundmachine. Then the operator, or an electronically controlled imageparameters monitor, can make adjustments to optimize the image. In someapplications, the relationship between the band-pass filter and z-offsetmay be known to within a certain degree of accuracy. This is analogousto the situation where variable resistors and capacitors are adjustedsimultaneously under a known relationship, which does not have to belinear.

The band-pass filter may be adjusted by digitally controlling variableresistors and capacitors in the filter to achieve the appropriate filtercharacteristics. In the alternative, a series of band-pass filters canbe employed and the filter circuit can switch between different filters;however, this is a more cumbersome approach. On the other hand, whilethis approach is cumbersome and less ideal in terms of having intervalsof filtration, more precise control at a given filtration setting isachievable because it is easier to compensate for variabilities from,for example, changes in resistor and capacitor noise.

As noted above, the polarization controller 216 may be driven, forexample, by a step motor 218, to perform polarization sensitive OCT(“PS-OCT”). It should be appreciated by those skilled in the art thatthis technique is applicable to both spectral domain OCT systems, and totime domain OCT system. Assessing biological tissues such as organizedcollagen, particularly in tendon, can benefit from having desiredcontrol over the polarization of light in the reference arm. As a briefoverview of the concept of polarization, polarized light can be viewedas consisting of x- and y-components, with the z-direction being thedirection of propagation. The birefringence, which may be used to assesstissue composition, refers to the change in phase of one componentrelative to the other, such as the x-component relative to they-component, as the light propagates through the tissue. Some tissues,such as organized collagen in particular, are highly birefringent. Mosttissue is not birefringent, however, and tissue that, for example, haslost its collagen organization loses its birefringence. Thus, loss ofcollagen organization in tendon, even if the tendon looks normal byvisual inspection, can be identified by PS-OCT, indicating pathologicchanges.

When the x- and y-components are combined in different relativeintensities and different phases, the end result can be linearlypolarized light of any axis (not just x or y), circularly polarizedlight (right or left), or elliptically polarized light. The polarizationcontroller 216 may be configured to change the polarization of the lightin the reference arm between these polarization states in a controlled,or well-defined, manner. Thus; the polarization controller 216 allowsfor the sweeping through these polarization states in a manner that canprovide the identification of an optimal polarization state for definingtissue organization. The approach may also be designed to insure minimumand maximum in backreflection intensity.

There are two different approaches for performing PS-OCT, single anddual channel. In brief, single detector PS-OCT measures changes in thebackreflection of light within tissue as the sample or reference armpolarization state is changed. As it does not depend on recording anabsolute value that can change when light propagates through the fibers,or tissue not of interest, but rather an image change as thepolarization is changed, it is relatively robust to artifacts and simpleto implement. Additional advantages over dual channel approaches arethat single channel approaches are minimally susceptible to fiberbending artifacts, are performed in real time, produce results that canbe read directly off the screen, and include an optical design that isrelatively simple making it less susceptible to internal artifacts suchas angular deviation of reflectors and filters.

Some understanding of how single detector PS-OCT is provided by example.With highly birefringent tissue, such as healthy tendon, bands occur inthe tissue as a result of rotation of the backreflected lightpolarization state as it passes through the tissue. In other words, inthis unusual circumstance, birefringence assessment does not demandreference arm polarization to be rotated. Rather, the peak-to-peakdistance in the image is a measure of birefringence. But for most othertissues relevant to this analysis technique, such as aged or diseasedtendon, the birefringence is lower. For these tissues, the distance overwhich the backreflected light rotates a single cycle is greater than thewidth of the imaging area; that is, band width is greater than tissuewidth. So, rather than using a single incident polarization state in thereference and sample arm, the polarization state of reference arm lightis rotated, for example, at a constant velocity. A measurement, such astime or change in polarization paddle position, to go from peak-to-peakat a given point in the image with rotation of reference armpolarization is a measure of tissue birefringence. That is, thereference arm is being rotated through a range of polarization stateswith the polarization controller 216, so that as this is occurs, thebackreflection of the sample arm is changing. If the birefringence inthe sample or tissue is high, the backreflection in the sample willchange rapidly with changes in the reference arm.

As stated, PS-OCT includes tailoring polarization rotation in thereference arm to improve assessment of tissue structure. Again,polarization is rotated between linear, circular, and elliptical statesin a controlled manner. By way of example, the polarization controller216 may be a standard Lefevre type fiber optic polarizer that can bechanged at a constant velocity. Such a polarization controller 216includes a certain length of single mode fiber spooled on three paddles.These paddles are adapted and connected to a driver 218, such as a stepmotor, that serves as a driver controller of angular position and rates.The driven paddles can be stepwise rotated back and forth within plus orminus ninety degrees, and with 0.9 degree steps, via a programmablemotion controller or through a computer processor. The paddle rotationrate is variable and controllable as described below. In a Lefevre typepolarization controller, two quarter-wave coils control the ellipticityand a half-wave coil controls the linear orientation. This type ofpolarization controller may be desirable because it has low polarizationmode dispersion (“PMD”), which at higher levels can impair theresolution of an OCT system. Motorization may be added to thepolarization controller to allow constant velocity rotation, with eachpaddle velocity being controlled separately.

Interference is maximum between the reference and sample arm whenpolarization is completely matched between the two arms. Therefore, ifthe sample arm contains one polarization state, at maximum interferencethe polarization of the reference and sample arm are the same. Second,because of this, polarization in the reference arm is determined throughthe use of polarization filters and retarders, which control phase, suchas quarter-wave plates in the sample arm.

As the polarization states is changed, data regarding this change can beplotted on a Poincare's sphere to represent the different polarizationstates as the paddles are rotated. In a Poincare's sphere, the northpole is right circularly polarized light, while the south is left; theequator represents the different linearly polarized states; and anyother position on the surface of the sphere is elliptically polarizedlight. If a data point is on the surface, attenuation is zero, and whenit is inside the sphere a finite amount of attenuation exists from thesample. A sweep of polarization between different states can be plottedand displayed on the sphere. It is contemplated that with this approach,a scanning pattern that optimizes the peaks from troughs during scanningcan be determined.

Note that these steps are done to establish the polarization sweep inthe reference arm. Once a sweep has been deemed as optimal for theimaging task at hand, the fibers are fixed in position, then paddlepositions and motor parameters kept constant. In other words, once thesweep is established, these steps do not need to be repeated. The actualsteps to get to this fixed reference arm sweep generally are as follows.

The paddles in the reference arm are moved to a fixed position. Thelinear polarizer in the sample arm is rotated through zero, ninety,forty-five, and negative forty-five degrees, consecutively. Thecorresponding interferogram is measured at each position. The linearpaddle position is then maintained in the reference arm. A quarter waveplate is inserted into the beam, and the fast axis is aligned at plus orminus forty-five degrees to the linear polarizer to obtain the right andleft circular polarization state, respectively. Again, interferogramsare measured. The paddles are then moved in the reference arm todifferent positions and the foregoing measurements are repeated. By wayof example, the sweep may be generated in approximately two seconds.

The present invention has been described in terms of one or morepreferred embodiments, and it should be appreciated that manyequivalents, alternatives, variations, and modifications, aside fromthose expressly stated, are possible and within the scope of theinvention.

1. An optical coherence tomography system comprising: a light sourceconfigured to produce light to illuminate a sample with the samplelight; at least one optical path configured to receive at least one ofreference light and sample light from the light source and to illuminatea sample with the received sample light; a detector in opticalcommunication with the at least one optical path and configured toreceive the reference and sample light; a processor coupled to thedetector and the light source and configured to: a) receive a signalfrom the detector; b) determine, from the received signal, aninterference signal related to the reference light and the sample light;c) receive a calibration signal from the light source; d) identify atleast one of a series of extrema and a series of crossing values in thereceived calibration signal; e) identify at least one of a series ofcalibration extrema and a series of calibration crossing values from thereceived calibration signal and the identified at least one of series ofextrema and series of crossing values by performing an interpolation; f)calibrate the interference signal using the identified at least one of aseries of calibration extrema and series of calibration crossing values;and g) reconstruct an image of the sample from the recalibratedinterference signal.
 2. The optical coherence tomography system asrecited in claim 1 in which the processor is configured to: e) identifya series of calibration extrema from the identified series of extremaand received calibration signal by performing a first interpolation, andto identify a series of calibration crossing values from the identifiedseries of zero-crossing values and received calibration signal byperforming a second interpolation; and f) calibrate the interferencesignal using the identified series of calibration extrema and series ofcalibration crossing values.
 3. The optical coherence tomography systemas recited in claim 2 in which the first interpolation performed by theprocessor in step e) includes a cubic spline interpolation.
 4. Theoptical coherence tomography system as recited in claim 2 in which thesecond interpolation performed by the processor in step f) includes asubstantially linear interpolation.
 5. The optical coherence tomographysystem as recited in claim 1 in which the interpolation performed by theprocessor in step e) includes at least one of a cubic splineinterpolation and a substantially linear interpolation.
 6. The opticalcoherence tomography system as recited in claim 1 in which the lightsource is configured to produce light over a range of wavelength values.7. The optical coherence tomography system as recited in claim 6 furthercomprising an interferometer coupled to the light source and configuredto produce the calibration signal as light is swept over the range ofwavelength values.
 8. The optical coherence tomography system as recitedin claim 1 in which the processor is further configured in step d) toperform a global optimization method to search for the estimated seriesof extrema and series of crossing values.
 9. The optical coherencetomography system as recited in claim 8 in which the global optimizationmethod performed by the processor in step d) is a genetic algorithm andstep d) further includes: d)i) defining a fitness function such thatdata values in the calibration signal that are near to extrema andcrossing values increase a fitness value for extrema and crossingvalues, respectively; d)ii) selecting a first generation; and d)iii)selecting a number of values during each successive generation based ontheir quality measured by the fitness function.
 10. The opticalcoherence tomography system as recited in claim 1 in which the at leastone optical path includes a reference path in optical communication withthe light source and configured to receive reference light therefrom anda sample path in optical communication with the light source andconfigured to receive sample light therefrom and to illuminate a samplewith the received sample light.
 11. The optical coherence tomographysystem as recited in claim 1 further comprising a logarithmic amplifierin communication with the light source and configured to receive andamplify therefrom a calibration signal, and in which the processor isconfigured to receive the amplified calibration signal from thelogarithmic amplifier.
 12. The optical coherence tomography system asrecited in claim 1 further comprising at least one of a logarithmicamplifier, a diode, and a transistor in communication with the detectorand configured to amplify the signal received therefrom, therebyincreasing a dynamic range of the signal, and in which the processor isconfigured to receive the amplified signal from the at least one of alogarithmic amplifier, a diode, and a transistor.
 13. The opticalcoherence tomography system as recited in claim 1 further comprising: adriver; and a polarization controller coupled to the driver and inoptical communication with the at least one optical path, thepolarization controller configured to change at least one of apolarization and an intensity of the at least one of reference light andsample light in the at least one optical path while being driven by thedriver.
 14. An optical coherence tomography system comprising: a lightsource; a detector; an interferometer in optical communication with thelight source and the detector; a logarithmic amplifier in communicationwith the light source and configured to receive and amplify acalibration signal therefrom; a processor in communication with thelogarithmic amplifier and the interferometer, the processor beingconfigured to: receive a spectral interference signal from the detector;receive the amplified calibration signal from the logarithmic amplifier;calibrate the received spectral interference signal using the receivedamplified calibration signal; and produce an image having at least oneof an improved resolution, an improved contrast, and an increaseddynamic range from the calibrated spectral interference signal.
 15. Theoptical coherence tomography system as recited in claim 14 in which thelight source includes an interferometer for producing the calibrationsignal.
 16. The optical coherence tomography system as recited in claim14 in which the light source is coupled to another interferometer thatis in communication with the logarithmic amplifier, and the anotherinterferometer produces the calibration signal from light received fromthe light source.
 17. The optical coherence tomography system as recitedin claim 14 in which the interferometer includes a reference arm and asample arm, and the reference arm includes a reflector configured to bedisplaced along an axis substantially perpendicular to the reflector.18. The optical coherence tomography system as recited in claim 14further comprising at least one of a logarithmic amplifier, a diode, anda transistor in communication with the detector and configured toamplify a signal received therefrom.
 19. The optical coherencetomography system as recited in claim 14 further comprising a band-passfilter in communication with the detector, the band-pass filter beingconfigured to filter a signal received from the detector.
 20. Theoptical coherence tomography system as recited in claim 19 in which theband-pass filter is a variable band-pass filter.
 21. The opticalcoherence tomography system as recited in claim 20 in which a passbandof the variable band-pass filter is determined using information relatedto a displacement of the mirror in the reference arm.
 22. The opticalcoherence tomography system as recited in claim 21 in which the mirrorin the reference arm is configured to be adjusted with the variableband-pass filter at least one of manually and computationally.
 23. Theoptical coherence tomography system as recited in claim 14 in which theprocessor is configured to calibrate the received spectral interferencesignal using the received amplified calibration signal by: i)identifying at least one of a series of extrema and a series of crossingvalues in the amplified calibration signal; ii) identifying a series ofcalibration extrema from the identified series of extrema and amplifiedcalibration signal by performing a first interpolation; iii) identifyinga series of calibration crossing values from the identified series ofzero-crossing values and amplified calibration signal by performing asecond interpolation; and iv) calibrating the spectral interferencesignal using the identified series of calibration extrema and series ofcalibration crossing values.
 24. The optical coherence tomography systemas recited in claim 14 in which the processor is further configured toidentify the series of calibration extrema and series of calibrationcrossing values by performing a global optimization method.
 25. A methodfor producing an image of a subject with an optical coherence tomography(OCT) system, the steps comprising: a) illuminating at least one of areference path of the OCT system and a sample path of the OCT systemwith a light source, the sample path being in optical communication withthe subject; b) identifying an interference signal from the referenceand sample paths of the OCT system; c) acquiring a calibration signalfrom light emitted by the light source; d) estimating a series ofextrema and a series of crossing values from the acquired calibrationsignal; e) identifying a first series of calibration characteristicsfrom the estimated series of extrema and amplified calibration signal byperforming a first interpolation; f) identifying a second series ofcalibration characteristics from the estimated series of crossing valuesand amplified calibration signal by performing a second interpolation;g) calibrating the interference signal using at least one of theidentified first and second series of calibration characteristics; andh) reconstructing an image of the subject using the calibratedinterference signal.
 26. The method as recited in claim 25 furthercomprising the step of logarithmically amplifying the calibration signalto produce an amplified calibration signal, and in which the series ofextrema estimated in step d) are estimated from the amplifiedcalibration signal.
 27. The method as recited in claim 25 furthercomprising the step of logarithmically amplifying the interferencesignal before calibrating the interference signal to increase a dynamicrange of the interference signal.
 28. The method as recited in claim 25in which step a) includes producing the wavelength of the light over arange of wavelength values.
 29. The method as recited in claim 28 inwhich step c) includes illuminating an interferometer as the lightsource produces the wavelength of the light over the range of wavelengthvalues in step a).
 30. The method as recited in claim 25 in which stepd) includes performing a global optimization method to search for the atleast one of the estimated series of extrema and series of crossingvalues.
 31. The method as recited in claim 30 in which the globaloptimization method in step d) is a search technique incorporating atleast one of a genetic algorithm and an artificial intelligencemodality, and step d) further includes: d)i) determining a fitnessfunction such that data values in the calibration signal that are nearto the at least one of the extrema and crossing values increase afitness value for the at least one of the extrema and crossing values,respectively; d)ii) selecting a first generation; and d)iii) selecting anumber of values during each successive generation based on theirquality measured by the fitness function.
 32. The method as recited inclaim 25 in which at least one of the series of calibrationcharacteristics includes at least one of zero-crossing values andDC-crossing values.
 33. The method as recited in claim 25 in which thefirst interpolation performed in step e) includes at least one of acubic spline interpolation, a Gaussian interpolation, and a polynomialinterpolation.
 34. The method as recited in claim 25 in which the secondinterpolation performed in step f) includes one of a linearinterpolation, a Gaussian interpolation, a polynomial interpolation, andspline interpolation.
 35. The method as recited in claim 25 in which thefirst and second series of calibration characteristics are distributedsubstantially uniformly along at least one of an abscissa and anordinate.
 36. The method as recited in claim 35 in which the at leastone of the abscissa and the ordinate represents at least one ofwavelength and wavenumber.
 37. The method as recited in claim 25 inwhich step g) includes forming a calibrated signal array from thosevalues in the interference signal associated with at least one of thefirst and second series of calibration characteristics.
 38. A method forproducing an image of a subject with an optical coherence tomography(OCT) system, the steps comprising: a) illuminating at least one of areference path of the OCT system and a sample path of the OCT systemwith a light source, the sample path being in optical communication withthe subject; b) identifying an interference signal from the referenceand sample paths of the OCT system; c) acquiring a calibration signalfrom light emitted by the light source; d) identifying at least onecharacteristic of the acquired calibration signal; e) identifying afirst series of calibration characteristics from the at least onecharacteristic of acquired calibration signal by performing a firstinterpolation; f) identifying a second series of calibrationcharacteristics from the at least one characteristic of acquiredcalibration signal by performing a first interpolation; g) calibratingthe interference signal using the first and second series of calibrationcharacteristics; and h) reconstructing an image of the subject using thecalibrated interference signal.
 39. The method as recited in claim 38 inwhich step d) includes identifying at least one of a series of extremaand a series of crossing values in the acquired calibration signal, stepe) includes identifying a series of calibration extrema from theestimated series of extrema and acquired calibration signal byperforming a first interpolation, step f) includes f) identifying aseries of calibration crossing values from the estimated series ofcrossing values and acquired calibration signal by performing a secondinterpolation, and step g) includes calibrating the interference signalusing at least one of the identified series of calibration extrema andseries of calibration crossing values.
 40. The method as recited inclaim 39 in which step d) includes performing a global optimizationmethod to search for the at least one of the estimated series of extremaand series of crossing values.
 41. The method as recited in claim 38 inwhich step a) includes producing the wavelength of the light over arange of wavelength values.
 42. The method as recited in claim 38 inwhich step c) includes illuminating an interferometer as the lightsource produces the wavelength of the light over the range of wavelengthvalues in step a).
 43. An optical coherence tomography systemcomprising: a light source; a detector; an interferometer in opticalcommunication with the light source and the detector; a driver; apolarization controller coupled to the driver and in opticalcommunication with the a reference arm of the interferometer, thepolarization controller being configured to change at least one of apolarization and an intensity of light in the reference arm as thepolarization controller is driven by the driver; a processor incommunication with the interferometer, the processor being configuredto: receive a spectral interference signal from the detector; andproduce an image from the spectral interference signal.
 44. The opticalcoherence tomography system as recited in claim 43 in which theprocessor is in communication with the driver and is further configuredto direct the driver to sweep the polarization controller through aplurality of polarization states.
 45. The optical coherence tomographysystem as recited in claim 44 in which the processor is furtherconfigured to select one of the plurality of polarization states as anoptimal polarization state for a particular sample being imaged by theoptical coherence system.